Conjecture C (Brevig, Ortega-Cerdà, Seip and Zhao [1]})  
The Riesz projection \(P_+\)  is a contraction from \(L^{p^{\prime }} (\)  to \(H^{\frac{4}{p}}\)  for all \(1 \le p < \infty \) , where \(p^{\prime } = \frac{p}{p-1}\) . If \(p = \infty \) , we have that
\(\exp \left( \dfrac{1}{2\pi } \int _0^{2\pi } \log \left| P_+ F (e^{it}) \right| \: dt \right) \le \Vert  F \Vert _{L^1},\) 
